Question: Which of the following numbers is a multiple of 14? ${48,49,56,81,91}$
Solution: The multiples of $14$ are $14$ $28$ $42$ $56$ ..... In general, any number that leaves no remainder when divided by $14$ is considered a multiple of $14$ We can start by dividing each of our answer choices by $14$ $48 \div 14 = 3\text{ R }6$ $49 \div 14 = 3\text{ R }7$ $56 \div 14 = 4$ $81 \div 14 = 5\text{ R }11$ $91 \div 14 = 6\text{ R }7$ The only answer choice that leaves no remainder after the division is $56$ $ 4$ $14$ $56$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $56$ $56 = 2\times2\times2\times7 14 = 2\times7$ Therefore the only multiple of $14$ out of our choices is $56$. We can say that $56$ is divisible by $14$.